Chapter 1 Review
Foundations
Learning vocabulary is an extremely important part of studying the math language. Much of the author's meaning is lost if the student doesn't understand the implications of a chosen word. Use the following tools to practice the vocabulary from Chapter 1.


Number Properties

Sets of Numbers

For any two real numbers a and b, a is greater than b if a is to the right of b on a number line.
Skill Check
To simplify fractions, divide out the greatest factor that is common to the numerator and denominator.
Skill Check
Add:
If the signs are the same, keep the sign and add the numbers. If the signs are different, subtract the numbers and give the answer the sign of the larger number
Subtract:
Change the subtraction to addition and write the opposite of the number that comes after i
Multiply/Divide:
Two negatives give a positive answer; a positive and a negative give a negative answer.
Skill Check 1
Skill Check 2
Skill Check 3
Skill Check 4
Skill Check 5
**Always reduce the answer to lowest terms. Unless otherwise stated, leave the answer as an improper fraction rather than changing it to a mixed fraction.**
Add/Subtract:
Find a common denominator. Add/Subtract the numerators. Keep the denominator.
Multiply:
Reduce any common factors in the numerator and denominator. Then multiply the numerators together and the denominators together.
Divide:
Leave the first fraction the way it is; change divide to times; write the reciprocal of (flip) the second fraction.
Try these:
Check your answer. 

Check your answer. 

Check your answer. 
Even powers of negative numbers:
Be very careful to distinguish between these problems. The placement of the parentheses makes a difference!

Base 
Exponent 
Evaluate 

3^{2} 
3 
2 
(3)(3) = 9 
( 3)^{2} 
 3 
2 
( 3)( 3) = 9 
 (3)^{2} 
3 
2 
 (3٠3) =  9

 3^{2} 
3 
2 
 (3٠3) =  9 
These will cause problems when you are evaluating expressions so be careful. If you are using a calculator, you must enter them correctly or the calculator will give you a wrong answer. Experiment with your calculator to be sure you can do it correctly.
Skill Check 1
Skill Check 2
Skill Check 3
Skill Check 4
Groups
These can be parentheses, brackets, absolute value bars, radicals, fraction numerator, or fraction denominator.
Powers and Roots
Evaluate any exponential expressions or radicals.
Multiply/Divide
Multiplication and division have the SAME level of importance. If both appear in a problem, work them from left to right.
Add/Subtract
Addition and subtraction have the SAME level of importance. If both appear in a problem, work them from left to right.
Try these. Be sure to ask questions, if you have trouble getting the correct answer.
Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
When evaluating expressions, rewrite the problem and put ( ) where there is a variable. Then fill in the parentheses with the given value for the variable. Remember the order of operations!
Try these.
Problem 1
Problem 2
An expression is undefined any time the denominator is equal to 0.
Skill Check 1
Skill Check 2
Add or subtract the coefficients of terms that have the same variable. Remember the sign stays with the number that comes after it.
Check your answer. 

Check your answer. 
Multiply the expression outside the parentheses times every term inside the parentheses. Watch for the minus sign. This is one of the most common sign errors!
Check your answer. 

Check your answer. 